# Interpretation of the THz-THz-Raman Spectrum of Bromoform

## TL;DR

This study interprets the THz-THz-Raman spectrum of bromoform using an improved RDM model, simplifying the analysis by a self-consistent time reference and eliminating the need for large multi-quanta dipole elements.

## Contribution

The paper introduces a self-consistent time coordinate framework and an analytical parametrization of the RDM model for better spectrum interpretation.

## Key findings

- Simplified spectrum analysis with a self-consistent time reference.
- Elimination of the need for large multi-quanta dipole matrix elements.
- Agreement of RDM parameters with ab initio calculations.

## Abstract

Nonlinear THz-THz-Raman (TTR) liquid spectroscopy offers new possibilities for studying and understanding condensed-phase chemical dynamics. Although TTR spectra carry rich information about the systems under study, the response is encoded in a three-point correlation function comprising of both dipole and polarizability elements. Theoretical methods are necessary for the interpretation of the experimental results. In this work, we study the liquid-phase dynamics of bromoform, a polarizable molecule with a strong TTR response. Previous work based on reduced density matrix (RDM) simulations suggests that unusually large multi-quanta dipole matrix elements are needed to understand the measured spectrum of bromoform. Here, we demonstrate that a self-consistent definition of the time coordinates with respect to the reference pulse leads to a simplified experimental spectrum. Furthermore, we analytically derive a parametrization for the RDM model by integrating the dipole and polarizability elements to the 4th order in the normal modes, and we enforce inversion symmetry in the calculations by numerically cancelling the components of the response that are even with respect to the field. The resulting analysis eliminates the need to invoke large multi-quanta dipole matrix elements to fit the experimental spectrum; instead, the experimental spectrum is recovered using RDM simulations with dipole matrix parameters that are in agreement with independent ab initio calculations. The fundamental interpretation of the TTR signatures in terms of coupled intramolecular vibrational modes remains unchanged from the previous work.